Question

which congruence theorems can be used to prove \\( \triangle efg \cong \triangle jhg \\)? select two options.
\\( \square hl \\)
\\( \square sas \\)
\\( \square sss \\)

Explanation:

Step1: Analyze vertical angles

$\angle EGF=\angle JGH$ (vertical angles are equal).

Step2: Check side - angle - side (SAS)

We know that $EF = JH$ (given by the marks on the sides), $\angle EGF=\angle JGH$ (from Step 1), and $FG = HG$ (given by the marks on the sides). So, by the SAS (Side - Angle - Side) congruence theorem, $\triangle EFG\cong\triangle JHG$.

Step3: Check side - side - side (SSS)

We cannot use SSS (Side - Side - Side) because we only know two pairs of sides are equal ($EF = JH$ and $FG = HG$) and we don't know about the third pair of sides ($EG$ and $JG$).

Step4: Check HL (Hypotenuse - Leg)

We cannot use HL (Hypotenuse - Leg) as there is no information indicating that these are right - angled triangles.

Answer:

SAS